I'm guessing this serie converges, but I'm having trouble finding a convergent serie to bound it with. The other convergence tests have failed and the use of the integral convergence criterion is forbiden. I know that if there is a serie to bound it with, it would be of the form

I don't know what approach you are using to prove pointwise convergence. However, if you are using the old fashioned epsilon delta argument, you will see that there is a dependence on x when x is near a singular value.